Metamath Proof Explorer


Theorem sgrpssmgm

Description: The class of all semigroups is a proper subclass of the class of all magmas. (Contributed by AV, 29-Jan-2020)

Ref Expression
Assertion sgrpssmgm Could not format assertion : No typesetting found for |- Smgrp C. Mgm with typecode |-

Proof

Step Hyp Ref Expression
1 sgrpmgm Could not format ( x e. Smgrp -> x e. Mgm ) : No typesetting found for |- ( x e. Smgrp -> x e. Mgm ) with typecode |-
2 1 ssriv Could not format Smgrp C_ Mgm : No typesetting found for |- Smgrp C_ Mgm with typecode |-
3 mgmnsgrpex Could not format E. x e. Mgm x e/ Smgrp : No typesetting found for |- E. x e. Mgm x e/ Smgrp with typecode |-
4 ssexnelpss Could not format ( ( Smgrp C_ Mgm /\ E. x e. Mgm x e/ Smgrp ) -> Smgrp C. Mgm ) : No typesetting found for |- ( ( Smgrp C_ Mgm /\ E. x e. Mgm x e/ Smgrp ) -> Smgrp C. Mgm ) with typecode |-
5 2 3 4 mp2an Could not format Smgrp C. Mgm : No typesetting found for |- Smgrp C. Mgm with typecode |-